Risk Management - April 27, 2011

Diversification matters... but not for risk

Since the global financial crisis of 2008, improving risk management practices— management of extreme risks, in particular—has been a hot topic. The postmodern quantitative techniques suggested as extensions of mean-variance analysis, however, exploit diversification as a general method. Although diversification is most effective in extracting risk premia over reasonably long investment horizons and is a key component of sound risk management, it is ill-suited for loss control in severe market downturns. Hedging and insurance are better suited for loss control over short horizons. In particular, dynamic asset allocation techniques deal efficiently with general loss constraints because they preserve access to the upside. Diversification is still very useful in these strategies, as the performance of well-diversified building blocks helps finance the cost of insurance strategies.

Risk management practices became a central topic after the financial crisis of 2008. Improvements to the methods of risk measurement, many of them made by industry vendors, have drawn on the literature on the modelling of extreme events (Dubikovsky et al. 2010; Zumbach 2007). Although there has been extensive research into extreme risk modelling in academe since the 1950s, it is only after difficult times that the financial industry becomes more open to alternative methods.

From an academic perspective, however, risk management decision-making goes beyond risk measurement and static asset allocation techniques. In fact, it can be argued that the non-classical methods are designed to use two basic techniques in finance—diversification and hedging—in a better way, and with the recent focus on post-modern quantitative techniques the role of diversification as a risk management tool has been over-emphasised. Even though it is a powerful technique, diversification has limitations that must be understood if unrealistic expectations for the real-world performance of risk management are to be avoided.

Although the idea behind it has long existed, a scientifically consistent framework for diversification, modern portfolio theory (MPT), was first posited by Markowitz (1952). Diversification—international diversification, sector and style diversification, and so on—has since become the pillar of many investment philosophies. It has also become a very important risk management technique, so much so that it is often considered, erroneously, synonymous with risk management. In fact, diversification as a general method is related to risk reduction as much as it is to improving performance and, therefore, it is most effective when it is used to extract risk premia. In short, it is only one form of risk management. The limitations of diversification stem from its relative ineffectiveness in highly correlated environments over relatively shorter horizons. Christoffersen et al. (2010) conclude that the benefits of international diversification across both developed and emerging markets have decreased because of a gradual increase in the average correlation of these markets. Thus, if international markets are well integrated, there is no benefit in diversifying across them.

The variations of correlation are important not only across markets but also over time; in the short run, then, relying on diversification alone can be dangerous. Over longer horizons, Jan and Wu (2008) argue that diversified portfolios on the mean-variance efficient frontier outperform inefficient portfolios, an argument that adds to the debate that time alone may not diversify risks.

The limitations of diversification mean that, in certain market conditions, it can fail dramatically. Using a conditional correlation model, Longin and Solnik (2001) conclude that correlations of international equity markets increase in bear markets. In severe downturns, then, diversification is unreliable. Furthermore, it is generally incapable of dealing with loss control. So enhancing the quantitative techniques behind it by using more sophisticated risk measures and distributional models can lead to more effective diversification but not to substantially smaller losses in crashes. Loss control can be implemented in a sound way only by going beyond diversification to hedging and insurance, two other approaches to risk management.

A much more general and consistent framework for risk management is provided by the dynamic portfolio theory posited by Merton (1969, 1971). The theory presents the most natural form of asset management, generalising substantially the static portfolio selection model developed by Markowitz (1952). Merton (1971) demonstrated that in addition to the standard speculative motive, non-myopic long-term investors include intertemporal hedging demands in the presence of a stochastic opportunity set. The model has been extended in several directions: with stochastic interest rates only (Lioui and Poncet 2001; Munk and Sørensen 2004), with a stochastic, mean-reverting equity risk premium and non-stochastic interest rates (Kim and Omberg 1996; Wachter 2002), and with both variables stochastic (Brennan et al. 1997; Munk et al. 2004).

In addition to these developments, recognising that long-term investors usually have such short-term constraints as maximum-drawdown limits, or a particular wealth requirement, leads to further extensions of the model. Minimum performance constraints were first introduced in the context of constant proportion portfolio insurance (CPPI) (Black and Jones 1987; Black and Perold 1992), and in the context of option-based portfolio insurance (OBPI) (Leland 1980). More recent papers (Grossman and Zhou 1996) demonstrate that both of these strategies can be optimal for some investors and subsequent papers generalise the model by imposing minimum performance constraints relative to a stochastic, as opposed to a deterministic, benchmark. Teplá (2001), for example, demonstrates that the optimal strategy in the presence of such constraints involves a long position in an exchange option.

The much more general and flexible dynamic portfolio theory leads to new insight into risk management in general and the role of diversification. In this framework, diversification provides access to performance through a building block known as a performance-seeking portfolio (PSP). Downside risk control is achieved by assigning state-dependent—and possibly dynamic—weights to the PSP and to a portfolio of safe, or risk-free, assets. In fact, since the latest financial crisis, there has been confusion among market participants not only about the benefits and limitations of diversification as a method for risk management but also about how the methods of hedging and insurance are related to diversification. In the attached paper, our goal is to review diversification and clarify its purpose. Going back to the conceptual underpinnings of several risk management strategies, we see that, in a dynamic asset management framework, diversification, hedging, and insurance are complementary rather than competing techniques for sound risk management.

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